The generator matrix
1 1 1 1 1 1 1 1 X 0 1 X 2X+2 1 1 1 X 2X X 2 1 1 1 1 1 1
0 X 2X+2 X+2 2X 3X+2 2 3X X+2 X 0 3X X 2X+2 X+2 3X 3X+2 X X X 2X 2 3X+2 X 0 2X+2
generates a code of length 26 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 25.
Homogenous weight enumerator: w(x)=1x^0+8x^25+108x^26+8x^27+1x^32+2x^36
The gray image is a code over GF(2) with n=208, k=7 and d=100.
This code was found by Heurico 1.16 in -3.24e-008 seconds.